TPGs grade coins based on wear. Variety attributions are included if you pay extra for them. BUT Die cracks (which are present on your coin) are not attributes. Therefore TPGs won't note them on the slab.
Die cracks (particularly those on your coin) are often obvious features which are of interest to a few collectors. Those collectors will see them. But they will probably not increase the value of your coin.
IMO only submit your coin to a TPG if you want it graded.
Do I recall correctly that CAC is/was considering using the number range 0 to 10 for their grades? And using tenths values to refine their opinions? So a coin could be graded by CAC as 5.6?
Nic-a-date will probably NOT work since it was formulated to work on coins struck in part with nickel. That pretty much limits its use to nickel 3-cent coins and 5-cent coins from 1866 through now.
$77 is Greysheet price (mid-AU) so you did well. Not often can you get a coin for Greysheet. And all the ribs are there on the III. So much the better.
EAC grading is a whole different world. But as I understand it, value is largely based on ANA grading. Problem is that ANA grading only takes into account the date and a particularly scarce or rare varieties. The EAC people refine that, hence they can pick up bargains that we ordinary collectors do know about.
Very nice coin. I collect large cents by variety so your coin gave me practice IDing the Newcomb number. I didn't do well. Starting about 1837 each year had a boatload of varieties.
But whatever, I'd gladly include your coin in my collection if it were mine.
IMO it's not collectible as is. Therefore any cleaning you do will not impair its value. If it were me, I would clean it and keep it as a space-filler until you get a good one.